Descartes' rule of signs, Newton polygons, and polynomials over hyperfields
Number Theory
2022-07-01 v4 Commutative Algebra
Abstract
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's "polygon rule".
Keywords
Cite
@article{arxiv.1811.04966,
title = {Descartes' rule of signs, Newton polygons, and polynomials over hyperfields},
author = {Matthew Baker and Oliver Lorscheid},
journal= {arXiv preprint arXiv:1811.04966},
year = {2022}
}
Comments
21 pages. v2: Revised the exposition and organization of the paper, corrected some minor typos. v3: Revised according to referee report, added new references. v4: Corrected a typo pointed out by Micha\"el Bensimhoun